202110721-PERFORM-STUDENT-WORKBOOK-MATHEMATICS-G08-FY_Optimized

practice workbook Mathematics Grade 8 Name: Roll No: Section: School Name:

by classklap IMAX is India’s only customised content and educational assessment m. 610+ Published Books Team of IITians & PhDs IMAX Program has authored about 610+ Content development and automation are publications which are used by more than led by a team of IITians, data scientists and 4,50,000+ students. education experts Workshops Lakh Assessments IMAX Program has conducted IMAX Program has conducted more than teacher training workshops for more 85,00,000+ assessments across 17 states in the last 10 years. than 15,000+ teachers. Copyright © 2020 BGM Policy Innovations Pvt Ltd) All rights reserved. No part of this publication, including but not limited to, the content, the presentation layout, session plans, themes, key type of sums, mind maps and illustrations, may be reproduced, stored in a retrieval system or transmitted, in any form or by any means (electronic, mechanical, photocopying, recording or otherwise), without the prior, written permission of the copyright owner of this book. This book is meant for educational and learning purposes. The author(s) of the book has/ have taken all reasonable care to ensure that the contents of the book do not violate any copyright or other intellectual property rights of any person in any manner whatsoever. In the event the author(s) has/have been unable to track any source and if any copyright has been inadvertently infringed, please notify the publisher in writing for any corrective action. Some of the images used in the books have been taken from the following sources www.freepik.com, www.vecteezy.com, www.clipartpanda.com Creative Commons Attribution This book is part of a package of books and is not meant to be sold separately. For MRP, please refer to the package price.

This practice book is designed to support you in your journey of learning Mathematics for class 8. The contents and topics of this book are entirely in alignment with the NCERT syllabus. For each chapter, a concept map, expected objectives and practice sheets are made available. Questions in practice sheets address different skill buckets and different question types, practicing these sheets will help you gain mastery over the lesson. The practice sheets can be solved with the teacher’s assistance. There is a self-evaluation sheet at the end of every lesson, this will help you in assessing your learning gap.



TABLE OF CONTENT • Assessment Pattern: 40 Marks • Assessment Pattern: 80 Marks • Syllabus & Timeline for Assessment Page 1: 1. Rational Numbers Page 11: 2. Linear Equations in One Variable Page 18: 3. Understanding Quadrilaterals Page 25: 4. Practical Geometry Page 30: 5. Data Handling Page 41: 6. Squares and Square Roots Page 49: 7. Cubes and Cube Roots Page 53: 8. Comparing Quantities Page 60: 9. Algebraic Expressions and Identities Page 67: 10. Visualising Solid Shapes Page 75: 11. Mensuration Page 82: 12. Exponents and Powers Page 87: 13. Direct and Inverse Proportions Page 93: 14. Factorisation Page 99: 15. Introduction to Graphs Page 108: 16. Playing with Numbers







ASSESSMENT PATTERN Marks: 40 Grade 8/Mathematics ASSESSMENT PATTERN Marks: 40 Grade 8 / Maths Max Internal PAPER: BEGINNER PAPER: PROFICIENT Mark Option Q.No Skill Level Difficulty Level Skill Level Difficulty Level Easy Medium Difficult Easy Medium Difficult Section A (Question Type: VSA) · ·· · · 11 Remembering · · Remembering · · · 21 Analysing · ·· · Analysing · · · Applying · 31 Applying · ·· Understanding ·· · · Understanding · ·· 41 Understanding ·· · Understanding · · Understanding · 51 Understanding Applying · · Remembering ·· 61 Understanding Applying · ·7 1 Understanding Remembering Applying Understanding 81 Applying 91 Remembering ·Section B (Question Type: SA) · Analysing 10 1 Applying Remembering Understanding ·11 2 Remembering Remembering 12 2 Understanding Understanding Remembering 13 2 Applying Remembering ·Section C (Question Type: SA)Analysing 14 3 15 3 Remembering ·16 3 Understanding Remembering 17 3 Section D (Question Type: LA) ·18 4 Understanding Remembering 19 4 20 4 Remembering Beginner Paper: (Easy: 40%, Medium: 50%, Di icult:10%) Proficient Paper: (Easy: 25%, Medium: 50%, Di icult: 25%) Easy Question (E): Direct reference to concept fact, definition, theories and laws (mostly from worked examples in the book or end of chapter exercise). Medium Di iculty Question (M): Combination of concepts, definition, theories and laws, solving through direct or indirect methods, numerical with direct substitution, drawing diagram and direct labelling, uses and applications, balance equation (mostly modified concepts). Di icult Question (D): Complex numerical, justification, interpret some info and draw diagram, working of appliance, functioning (on-the-fly thinking of solutions based on understanding of concepts).

AASSSSEESSSSMMEENNTTPPAATTTTEERRNN MMaarkrks:s:8800 Grade 8/GMraatdheem8 /atMicasths Max Internal PAPER: BEGINNER PAPER: PROFICIENT Mark Option Q.No Skill Level Difficulty Level Skill Level Difficulty Level Easy Medium Difficult Easy Medium Difficult Section A (Question Type: MCQ) 11 Remembering • Remembering • 21 Remembering • Remembering • 31 Remembering • Remembering • 41 Applying • Applying • 51 Understanding • Understanding • 61 Remembering • Remembering • 71 Understanding • Understanding • 81 Understanding • Understanding • 91 Analysing • Analysing • 10 1 Remembering • Remembering • Section B (Question Type: VSA) 11 1 • Understanding • Understanding • 12 1 Analysing • Analysing • 13 1 • Applying • Applying • 14 1 Applying • Applying • 15 1 Applying • Applying • 16 1 • Understanding • Understanding • 17 1 Analysing • Analysing • 18 1 Applying • Applying • 19 1 Understanding • Understanding • 20 1 • Remembering • Remembering • Section C (Question Type: SA) 21 2 Remembering • Remembering • 22 2 Understanding • Understanding • 23 2 Remembering • Remembering • 24 2 • Analysing • Analysing • 25 2 • Applying • Applying • 26 2 Applying • Applying • Section D (Question Type: SA) 27 3 • Remembering • Remembering • 28 3 • Remembering • Remembering • 29 3 • Understanding • Understanding • 30 3 Remembering • Remembering • 31 3 Remembering • Remembering • 32 3 Remembering • Remembering • 33 3 • Applying • Applying • 34 3 Analysing • Analysing • Section E (Question Type: LA) 35 4 • Understanding • Understanding • 36 4 • Understanding • Understanding • 37 4 Remembering • Remembering • 38 4 Understanding • Understanding • 39 4 Understanding • Understanding • 40 4 Understanding • Understanding •

SYLLABUS FOR ASSESSMENT Grade 8/Mathematics CHAPTERS PT-1 TE-1 PT-2 TE-2 1. Rational Numbers ✓ ✓ ✓ 2. Linear Equations In One Variable ✓ ✓ ✓ ✓ 3. Understanding Quadrilaterals ✓ ✓ ✓ ✓ 4. Practical Geometry ✓ 5. Data Handling ✓ ✓ ✓ ✓ 6. Squares and Square Roots ✓ ✓ 7. Cubes and Cube Roots ✓ ✓ ✓ 8. Comparing Quantities ✓ 9. Algebraic Expressions and Identities ✓ ✓ 10. Visualising Soild Shapes ✓ ✓ 11. Mensuration ✓ 12. Exponent and Powers ✓ 13. Direct and Inverse Proportions ✓ 14. Factorisation ✓ 15. Introduction to Graphs ✓ 16. Playing with Numbers Assessment Timeline Periodic Test-1 : 22nd July to 12th August Term 1 Exam : 23rd September to 21st October Periodic Test-2 : 16th December to 13th January Term 2 Exam : 1st March to 30th March



LESSON WISE PRACTICE SHEETS (This section has a set of practice questions grouped into different sheets based on different concepts. By solving these questions you will strengthen your subject knowledge. A self-evaluation sheet is provided at the end of every lesson.)



1. Rational Numbers Learning Outcome By the end of this chapter, you will be: • Apply the properties of rational numbers to solve • Explain the different properties of rational numbers. problems. • Compute the additive and multiplicative inverse of • Locate a given rational number on a number line. a given rational number. • Calculate required number of rational numbers between two given rational numbers. Concept Map Properties of Rational Additive Identity Multiplicative Identity Numbers Additive Inverse Multiplicative Inverse Closure Rational Numbers Commutativity Associativity Number line Finding rational numbers Distributivity Representation between two rational numbers By Making Common Denominator By repeated Averaging Key Points For any two rational numbers, a • Natural numbers are numbers such as 1, 2 , 3 , ….. and b, a is not always a rational Natural numbers with zero are whole numbers. b 10 Whole numbers with negative numbers are called number if b = 0. If zero is excluded, 3 4 = integers. 53 then rational numbers are closed • Rational numbers which can be expressed in the under division. 2 form of p , where p and q are integers and q ≠ 0. A number divided by zero is not q defined. i.e. a ÷ 0 is not defined. Example: 4 , 0,  2, 5, 15 5 , 8 ,}}} Closed under Natural Whole Integers Rational , Numbers Numbers Numbers 6 16 6 3 • Properties of Rational Numbers Addition Yes Yes Yes Yes o Closure Property Subtraction No No Yes Yes For any two rational numbers a, b, 2 4 22 Multiplication Yes Yes Yes Yes a + b is also a rational number.  No No (But Hence rational numbers are closed Division No No if zero is under addition. 3 5 15 excluded For any two rational numbers a, 2  5 7 o Commutativity § 2 ·  § 4 · then Yes) b, a−b is also a rational number. 33 3 Addition is commutative for ¨© 3 ¸¹ ©¨ 5 ¹¸ Hence rational numbers are closed 25 u 1 5 rational numbers. 22 under subtraction. 65 6 For any two rational numbers a, b § 4 ·  § 2 · 15 For any two rational numbers a, b, we have a + b = b +a ¨© 5 ¸¹ ¨© 3 ¸¹ 22 a × b is also a rational number. 15 Hence rational numbers are closed under multiplication. 1

1. Rational Numbers Subtraction is not commutative § 2 ·  § 5 · 7 o Additive Identity for rational numbers. ¨© 3 ¸¹ ©¨ 3 ¸¹ 3 Zero is called the identity for addition of rational For any two rational numbers a, b we have a−b ≠ b−a § 5 ·  § 2 · 7 numbers. It is also the additive identity for ¨© 3 ¹¸ ©¨ 3 ¸¹ 3 integers and whole numbers as well. For any number rational number ‘a’, we have a+0=0+a=a Multiplication is commutative for § 25 · u § 1 · 5 o Negative of a number or Additive Inverse of a rational numbers. ©¨ 6 ¸¹ ¨© 5 ¸¹ 6 For any two rational numbers a, b number we have a × b = b × a § 1 · u § 25 · 5 Negative or additive inverse of a number which ¨© 5 ¹¸ ©¨ 6 ¹¸ 6 when added to the given number will give zero as result. Division is not commutative for 4 rational numbers. 2 2 For a rational number of the form a the additive For any two rational numbers, a, 0.5 b b we have a ≠ b (or) a ÷ b ≠ b ÷ a 2 inverse is −a . Also for the rational number −a , 4 ba b a , Hence we can say b the additive inverse is b Commutativity Natural Whole Integers NRuamtYYNieeoobssnear sl E35abxam©¨§53pable·¸¹0: Ad§©¨ diabti¹·¸ve a0 of 3 is −3 such that Addition Numbers Numbers b 5 5 Subtraction Yes inverse Multiplication Yes Yes No No No Yes Yes Yes Division No No No No o Multiplicative Identity One is the multiplicative identity for rational o Associativity § § 2 ·  § 4 · ·  § 1 · 23 Addition is associative for ¨ ¨© 3 ¸¹ ¨© 5 ¸¹ ¸ ¨© 15 ¹¸ 15 numbers. It is also the multiplicative identity for rational numbers. © ¹ 23 integers and whole numbers. For any three rational 15 For any rational number ‘a’, we have a × 1 = 1 × numbers a, b, c we have § 2 ·  § § 2 ·  § 1 · · a=a (a + b) + c = a + (b+ c) ©¨ 3 ¹¸ ¨ ¨© 5 ¸¹ ©¨ 15 ¹¸ ¸ © ¹ o Reciprocal or Multiplicative inverse Reciprocal or multiplicative inverse of a number Subtraction is not § § 2 ·  § 5 · ·  § 1 · 8 associative for rational ¨ ©¨ 3 ¸¹ ¨© 3 ¸¹ ¸ ©¨ 3 ¸¹ 3 which when multiplied to the given number will numbers. © ¹ give one as result. For any three rational Zero has no reciprocal or multiplicative inverse. numbers a, b, c we have § 2 ·  § § 5 ·  § 1 · · 6 For a non zero rational number of the form a , if (a−b)−c ≠ a−(b−c) ¨ 3 ¸ ¨ ¨ 3 ¸ ¨ 3 ¸ ¸ 3 © ¹ © © ¹ © ¹ ¹ b Multiplication is § § 25 · u § 1 · · u § 1 · 5 c is the multiplicative inverse then associative for rational ¨ ©¨ 6 ¸¹ ©¨ 5 ¹¸ ¸ ¨© 2 ¸¹ 12 d numbers. © ¹ For any three rational § 25 · u § § 1 · u § 1 · · 5 a u c c u a 1 numbers a, b, c we have ¨© 6 ¸¹ ¨ ¨© 5 ¹¸ ©¨ 2 ¹¸ ¸ 12 (a × b) × c = a × (b × c) © ¹ Division is not associative bd d b for rational numbers. (4 ÷ 2) ÷ 2 = 1 For a non zero rational number of the form a For any three rational 4 ÷ ( 2 ÷ 2) = 4 numbers, a, b, c we have the multiplicative inverse is b . b (a ÷ b) ÷ c ≠ a ÷ (b ÷ c) a o Distributivity of Multiplication over Addition for rational numbers For any three rational numbers a, b, c, we have Natural Whole Rational a(b + c) = ab + ac (Distributivity of Multiplication Associativity Numbers Numbers Integers Numbers over Addition) Addition Yes Yes Yes Yes a(b−c) = ab−ac (Distributivity of Multiplication Subtraction No No No No over Subtraction) Multiplication Yes Yes Yes Yes Division No No No No 2

1. Rational Numbers • Representation of Rational Numbers on Number and c are M  1 , M  2 ,}., N  1 Line d PP P Any rational number can be represented on the Example: To find 3 rational numbers between number line. 1 and 3 . In a rational number, the number below the bar 24 (denominator), indicates the number of equal parts into which the main unit (of integer number 1 1 u 20 20 line) has been divided. 2 2 u 20 40 3 u 10 30 The number above the bar (numerator) indicates 3 4 u 10 40 many divisions should be considered for locating 4 the given number. The denominators have been equalized and Example 1: To represent 3 on a number line. there are 3 integers between the values of the 5 numerators (20 and 40). The rational numbers between 1 and 3 are The main unit (0 to 1, 1 to 2, -1 to 0, etc) are 24 divided into 5 (denominator of the given number) 21 22 23 39 parts each. The third division mark is selected , , ,….., . (numerator of the given number is 3.) among the 40 40 40 40 divided portions. From these numbers any three can be selected. If instead of turning the denominator to 40, the denominator can be obtained as 4000, 5000, or any other higher number. Accordingly the value of the numerator also increases and hence more rational numbers can be obtained between given numbers. In the number line shown, 1 is also equal to 5 and o Averaging or Division Method 5 L et a, b are the two rational numbers such that the next divisions can be numbered as 678 , , ,…… 555 • Rational numbers between two Rational Numbers There are countless rational numbers between any two given rational numbers. o Making common denominator method: Let a and c be two rational numbers between bd which ‘n’ number of rational numbers are to be found. Multiply and divide the numerator and denominators of the given rational numbers such their denominators become equal after the multiplication. Let M and N are the modified rational PP numbers of the given numbers. Here a = M and c = N bP dP The numbers M and N should be such that there are required numbers of integers between them. If M > N then the rational numbers between a b 3

1. Rational Numbers b > a, then a + b will also be a rational number and will be present between a and b, i.e., a  a  b  b . 22 Repeating this using newly obtained rational numbers and given rational numbers, countless rational numbers can be obtained between any two given rational numbers. Example: To find 3 rational numbers between 1 and 3 . 24 13 5  8 Rational number between given numbers is 2 4 2 15  Another rational number is 2 8 9 2 16 53  Another rational number is 8 4 11 2 16 4

1. Rational Numbers Work Plan CONCEPT COVERAGE COVERAGE DETAILS PRACTICE SHEET Pre-requisite Knowledge: • Natural numbers, Whole numbers, Integers PS – 1 Number System • Integer number line • Addition and subtraction of fractions • Multiplication and Division of rational numbers Rational Numbers • Properties of rational numbers PS – 2 • Representing Rational Numbers on Number line PS – 3 • Rational Numbers rational number on number PS – 4 line Worksheet for “Rational Numbers” PS – 5 Evaluation with Self Check or ---- Self Evaluation Sheet Peer Check* PRACTICE SHEET - 1 (PS-1) 1. Natural numbers start with ________, whereas whole numbers start with ____________ 2. In a number line all positive integers lie on __________ of ‘0’. 3. While subtracting integers the sign of the resulting number is sign of the ___________. 4. Multiplying a positive integer and a negative integer will result in _________ integer. 5. ‘0’ is greater than _________ integers and is less than all __________ integers. 6. Represent -6 and 6 on number line 7. The LCM of 6 and 12 is _____. 8. HCF of 4 and 12 is ________. 9. Express −3 as a fraction with numerator -15. 5 10. Express −42 as a fraction with denominator -16. 96 11. Subtract 4 from 9 . 77 12. Add −8 and 3 . 15 5 13. Add 2 and �3 and subtract the sum from −3 . 34 5 14. Multiply 3 by the reciprocal of −7 . 5 15 15. Divide − 8 and � 16 . �− 23 46 5

PRACTICE SHEET - 2 (PS-2) 1. Identify the properties in each case: i) § 2 u 3 · u 1 2 u § 2 u 1 · ii)§©¨ 3 u 4 · § 4 u 3 · ¨ 3 4 ¸ 5 3 ¨ 4 5 ¸ 5 7 ¹¸ ©¨ 7 5 ¹¸ © ¹ © ¹ iii)¨§ 2  1 · u 8 § 2 u 8 ·  § 1 u 8 · iv) 5 u § 8  3 · § 5 u 8 ·  § 5 u 3 · © 5 4 ¸ 11 ¨ 5 11 ¸ ¨ 4 11 ¸ 2 ¨ 14 7 ¸ ¨ 2 14 ¸ ¨ 2 7 ¸ ¹ © ¹ © ¹ © ¹ © ¹ © ¹ 2  2 0 v) 3 u 7 1 vi) 77 73 2 u 3  1 u 3  1 2 u 2. Solve using suitable properties: 5 7 6 2 14 5 3. Solve using suitable properties 91 21 49 24 uuuu 52 83 55 83 4. Solve using suitable properties i )� ¨§©  125  29 ·  125 3455 128 137 ¹¸ 128 � � � � � � � � � � � ii)� u u u 5534 5. Write the additive and multiplicative inverse of 1. 6. Write the additive and multiplicative inverse of −6 5 7. To get 1, we should multiply −8� by ? 21 PRACTICE SHEET - 3 (PS-3) 1. Represent the following on number line: 3 , 1 , 7 , 10 555 5 2. Represent the following on number line: −3 , −1 , −13 , −5 77 7 7 3. Represent the following on number line: 1 , 3 , 8 , −2 −5 , −8 66 6 6 6 6 PRACTICE SHEET - 4 (PS-4) 1. Find 5 rational numbers between 3 and 4 . 55 2. Find 5 rational numbers between 1 and 2 . 35 3. Find 5 rational numbers between 2 and 3. 4. Find 4 rational numbers between 3 and 1 using averaging method. 3 5. Find 3 rational numbers between −1 and 1 using average method. 22 6

PRACTICE SHEET - 5 (PS-5) I. Choose the correct option. 1. For which property of rational numbers is the equation 1 § 3  1 · § 1 u 3 ·  § 1  1 · an example? 4 ©¨ 8 5 ¹¸ ¨© 4 8 ¹¸ ¨© 4 5 ¸¹ (A) Commutative property of addition. (B) Closure property of addition. (C) Distributive property of multiplication over addition. (D) Associative property of addition. 2. Identify the correct statement with respect to rational numbers. (A) Addition of rational numbers is commutative. (B) Subtraction of rational numbers is not commutative. (C) Multiplication of rational numbers is associative. (D) All of these 3. Choose an example for the distributive property of rational numbers. 1§3  1· § 1 u 3 ·  § 1 u 1 · 4 ©¨ 8 5 ¹¸ ©¨ 4 8 ¸¹ ¨© 4 5 ¹¸ (A) 1 § 3  1 · § 1 u 3 ·  § 1 u 1 · 4 ©¨ 8 5 ¸¹ ¨© 4 8 ¹¸ ¨© 4 5 ¹¸ (B) 1 § 3  1 · § 1 u 3 ·  § 1 u 1 · 4 ¨© 8 5 ¸¹ ¨© 4 8 ¸¹ ¨© 4 5 ¹¸ (C) 1 § 3  1 · § 1  3 · u § 1  1 · 4 ¨© 8 5 ¹¸ ©¨ 4 8 ¹¸ ©¨ 4 5 ¸¹ (D) 5 4. Which of the following is the additive inverse of the rational number 13 ? 13 5 5 13 − (B) 13 − (D) 5 (A) 5 (C) 13 5. Find a rational number −5 between −15 and ? 11 11 9 11 13 4 3 17 − ,− ,− − ,− ,− (A) 11 11 11 (B) 11 11 11 2 15 16 5 10 18 − ,− ,− − ,− ,− (C) 11 11 11 (D) 11 11 11 −18 6. The multiplicative inverse of 153 is ________. 18 153 (C) −153 18 − (B) − 18 18 (D) 153 (A) 153 73 7. The product of 4 8 and the reciprocal of 10 is __________. 4 4 65 4 (A) 65 (B) 65 (C) 4 (D) − 65 7

PRACTICE SHEET - 5 (PS-5) 11 8. How many rational numbers are there between 9 and (− ) ? 9 (A) 2 (B) 10 (C) 19 (D) Infinitely many 9. If ‘p’ and ‘q’ are two rational numbers, then a rational number between ‘p’ and ‘q’ is given by ____________.  pq pq p+q p−q (C) 2 (D) 2 (A) 2 (B) 2 57 10. The product of the additive inverse of 8 and the multiplicative inverse of 8 is __________. (A) §  5 · 8 35 56 ©¨ 7 ¹¸ (B) 7 (C) 56 (d) 35 II. Short Answer Questions. 11. Write 4 rational numbers smaller than -6. 12. Given rational number − 3 , show that division is not closed. 10 13. Given rational numbers 512 and − 231 , show that subtraction is not commutative. 196 210 III. Long Answer Questions. 14. Use an appropriate property to find 8 8  5 89 u u 7 17 119 17 7 15. Find two rational numbers between − 11 and 5 . 15 − 12 8

SELF-EVALUATION SHEET Marks: 15 Time: 30 Mins 1. State whether the following statements are 4. Find 5 rational numbers between 1 and 2 True/ False. 10 10 i) Division of rational numbers is associative. such that the denominators of the rational ii) Multiplicative identity of rational numbers are 100.(2 Marks) numbers is 1. iii) Distributivity of addition over Multiplication is possible in rational numbers. iv) 0 is the additive identity for natural numbers and rational numbers. (2 Marks) 2. Give two rational numbers whose multiplicative inverse is equal to the number itself. (2 Marks) 5. Find 1 rational number between 2 and 8 using 79 common denominator method and average method. (2 Marks) 3. Represent 3 and −1 on a number line. 44 (2 Marks) 9

SELF-EVALUATION SHEET Marks: 15 Time: 30 Mins 6. Mention the property which can be used to 8. If a, b are two rational numbers, then a + b simplify the given rational number: 3 4 u 3  4 u 4 (2 Marks) 37 37 always represents a rational number between the numbers a, b. State True/False. Justify with example.(1 Mark) 7. Find the multiplicative inverse of the rational number. 3  42  5 Also state the properties u 7 357 used.(2 Marks) 10

2. Linear Equations in One Variable Learning Outcome • Explaining the meaning of linear equation and defining the meaning of linear equation in one By the end of this chapter, you will be: variable. • Transpose the terms to find the solutions of linear • Explaining the solution of a linear equation. equations. • Solve linear equations which have linear • Solve linear equations in one variable. • Form linear equations from given situation to expressions on one side and numbers on the other side. frame the equation and solve the equation to find • Solve linear equation by balancing the equation solution. by adding or subtracting the terms on both sides. • Explain the meaning of variable and constants • Solve applications based problems on with example. applications. Concept Map Key Points 3x = 20−5 3x = 15 • A linear equation is an algebraic equation in which x=5 each term is either a constant or the product of a o Variables on both sides constant and a variable. Bring all quantities with variables on side of the Example: x+8=10, 2y–5=15 equation and the left out quantities on the other side. Now, solve the equation to obtain the solution. • An equation of the form ax + b = 0 where a, b are Example: 3x + 6 = 2x + 10 real numbers such that ‘a’ should not be equal to Transposing variables and constants zero is called a linear equation. 3x−2x = 10−6 • The highest power of the variable in these x=4 expressions is 1. • Reducing complex equations to simpler form • Transposition method Example : x  y  8x 17 5x Constants or variables are transposed from one  side of the equation to other until the solution is 3 62 obtained. o Variables on one side and constant on one Transpose 5x to LHS side. 2 Example: 3x + 5 = 20 x  7  8x  5x 17 326 11

2. Linear Equations in One Variable Transpose 7 from LHS to RHS x  8x  5x 17 7 326 On solving both the sides, we get 5x 25  66 Thus, x = –5 is the required solution. • Word Problems on linear equations Converting word problems into linear equations to find the solution Example: Sum of two numbers is 70. One of the numbers is 10 more than the other number. What are the numbers? Let the numbers be x and 70-x, According to the question 70−x = x + 10 70−10 = x + x 60 = 2x 60 x= 2 x = 30, other number is 70−30 = 40 Work Plan CONCEPT COVERAGE COVERAGE DETAILS PRACTICE SHEET Pre-requisites Knowledge – • Variable, Constants, Algebraic expression, PS – 1 Algebraic expressions Transposition, BODMAS • What is of linear equation in one variable? PS – 2 • Solving linear equations which have linear expressions on one side and numbers on the other side • Solving application problems Linear Equations in one Variable • Solving linear equations having the variables PS – 3 on both sides • Solving application problems • Reducing equations to simpler form PS – 4 • Reducing equations to linear form PS – 5 Worksheet for “Linear Equations in One Variable” PS – 6 Evaluation with Self Check or ---- Self Evaluation Sheet Peer Check* 12

PRACTICE SHEET - 1 (PS-1) 1. Simplify vi) 3(5x + 4)−9x vii) 3 (x−4)−5 (6−2x) i) 3x−5 + 3−5x viii) 5 (x + 4)−9 (x−3) ii) 45  3y ix) 23  5x  9 x) 34x  5  6x iii) 5y−9 + 6−4y iv) 3−4(8−3x) v) 2x−9 + 4−7x PRACTICE SHEET - 2 (PS-2) 1. Simplify: i) x  8 14 ii) x  7 20 iii) 2x  8 14 iv) 3x  9 15 2. Perimeter of a rectangle is 52 m. If the length is 6 m longer than breadth, find the dimensions of rectangle. 3. Two numbers are in the ratio 7:8. If the sum of the numbers is 45, find the numbers. 4. Sum of two numbers is 70. If one number exceeds other number by 10, find the numbers. 5. One of the angles of a triangle is equal to the sum of other two angles. If other two angles are in the ratio 4:5, find all the angles of the triangle. 6. The unequal side of an isosceles triangle is 4 cm more than its equal sides. If the perimeter of the triangle is 22cm. Find the sides of the triangle. 7. The sum of five consecutive numbers is 140. Find the numbers. 8. The sum of three consecutive multiples of 6 is 108. Find the numbers. 9. The length of a rectangle is twice its breadth. If the perimeter is 72 m, find the dimensions of rectangle. 10. Akash’s father is 35 years younger than Akash’s Grandfather, and 25 years older than Akash. If the sum of their ages is 130 years. Find their present ages. 11. The length and breadth of a rectangular park are in the ratio of 3:2. If the cost of fencing the park at the cost of Rs 15 per m is Rs 6000, find the cost of laying the grass at the cost of Rs 10 per m2. 12. The average of three odd successive numbers is equal to 129. What is the largest of the three numbers? 13. Arun has Rs. 1, Rs. 2 and Rs 5 coins. Number of Rs 1 coins is half the numbers of Rs. 2 coins, Rs 5 coins are one third the number of Rs 2 coins. If the total value of money is Rs 125, find the number of coins of each type. 14. The sum of a positive even integer and the next third even integer is equal to 150. Find the number. 15. The numerator of a fraction is 2 more than its denominator. If 1 is added to the numerator the fraction becomes 2. Find the fraction. 13

PRACTICE SHEET - 3 (PS-3) 1. Solve the following i) 4x  5 7  3x ii) 5x  4 3x  2 iii) 22x  4 3x  8 iv) 2x  4 3x  8 v) 5x  5 2x  6 2. Ravi’s mother is four times as old as Ravi. After 5 years, his mother will be three times as old as him by then. Find their present ages. 3. Rani is 6 years older than her younger sister. After 10 years, the sum of their ages will be 50 years. Find their present ages. 4. The length of the rectangle exceeds its breadth by 3 cm. If the length and breadth are each increased by 2 cm, then the area of new rectangle will be 70 sq. cm more than that of the given rectangle. Find the length and breadth of the given rectangle. 5. Ten more than three times a number is equal to twenty less than six times the number. Find the number. 6. The average of 35, 45 and x is equal to five more than twice x. Find x PRACTICE SHEET - 4 (PS-4) 1. Solve: 23  4x  32  4x 2 2. Solve: - 4x  5  6 65  x 3. 2x  4 1 Solve : 33 4. Solve : x  2 8 3 5. Solve : 2x  3 5 5 6. Solve: 45x  8  10x 24 14

PRACTICE SHEET - 5 (PS-5) 1. Solve : 8  3x 6  2x 36 2. Solve : 2x  5 2 3x  5 5 3. Solve : 2x  6 6 5  3x 5 4. Solve : 4 8 3x  6 5x  7 5. 2x 5 4x 6 Solve : 54 6. 4 of a number is more than 3 of the number by 5. Find the number. 54 7. Ram is 46 years old. He is 4 years older than thrice his son’s age. Find the age of his son. PRACTICE SHEET - 6 (PS-6) I. Choose the correct option. 1. Choose the linear equation in one variable. (A) 2x +3y = 15 (B) 5a² – 2b = -27 (C) 17p – 34 = 0 (D)All of these 2. The value of the variable that satisfies a given linear equation is called its _______. (A) root (B) evaluation (C) solution (D) Both (A) and (B) 3. Which of these is a linear equation in‘t’? (A)19 – 15t = 45 (B) 84 t² + 34 = -236 (C)14t² + 5t = -125 (D) 234 t + 146 t³ = 0 4. Identify the value of the variable that satisfies the equation 5m – 12 = 23. (A)7 (B) -7 (C) 35 (D) −11 5 5. Identify the linear equation that correctly represents the following statement. “Four times a number is five more than the number.” (A) 4m = m – 5 (B) 4m + 5 = m (C)4m + m = 5 (D) 4m = m + 5 6. The statement for 5x – 12 = 2x is _____________. (A) 12 less than five times a number is twice the number itself. (B) 12 more than five times a number is twice the number itself. (C) Twice the difference of a number and 12 is less than five times the number itself. (D) 12 less than a number is twice the number itself. 7. The root of 4S  7 5 is __________. 8 8 15 3 5 (A) S = 8 (B) S = (C) S = (D) S = 2 w 8 8 8 8. Identify a linear equation that has the same root as 15r – 30 = 45. (A) 21w + 42 = 18 (B) 10g + 25 = 43 (C) 12a – 20 = 40 (D) Both (B) and (C) 9. The value of ‘k’ in the equation 3k – 5 = k + 7 is ____________. (A) – 12 (B) 12 (C) -5 (D) 6 10. The solution of a linear equation can be a/an __________. (A) equation only (B) rational number (C) whole number only (D) integer only II. Short Answer Questions. 11. Frame a linear equation in the variable ‘l’ for the given statement and solve it. The total surface area of a cube of side‘l’ cm is 294 cm². 12. Find the solution of14 r – 10 = 18 13. The sum of two numbers is 84. The smaller number is 10 less than the larger number. Find the numbers. III. Long Answer Questions. 8 14. Which number must be subtracted from 15 to get −7 ? 12 15. Find three consecutive multiples of 7 whose sum is 273. 15

SELF-EVALUATION SHEET Marks: 15 Time: 30 Mins 1. Solve for x:  (1 Mark) 5x  4 3x  2  23  x 4. Five years ago, John’s age was half of the age he will be in 8 years. How old is he now?  (2 Marks) 2. Solve for x: (1 Mark) 2x  5 11  3x 3 5. Solve for x:  (3 Marks) x  2x  3x 12 24 5 5 3. Solve for x:  (2 Marks) 3x  2 1 4x  3 2 16

SELF-EVALUATION SHEET Marks: 15 Time: 30 Mins 6. The digits of a 2-digit number differ by 5. If the digits are interchanged and the resulting number is added to the original number, we get 99. Find the original number.  (3 Marks) 7. The numerator of a rational number is 9 less than its denominator. If 3 is added to numerator and 5 is added to denominator, the fraction becomes 1 . Find the original number.  2 (3 Marks) 17

3. Understanding Quadrilaterals Learning Outcome By the end of this chapter, you will be: • Understand the properties of quadrilateral. • Classify the types of polygon. • Understand the difference in properties of angles • Understand the difference between convex and and sides of a quadrilateral. concave polygon. • Understand the properties of parallelogram and • Learn to find the exterior angles of a polygon. its types. Concept Map Understanding Quadrilaterals Polygon Quadrilateral Kite – Quadrilateral Four Sided Polygons with exactly two pairs of consecutive equal Parallelogram – Quadrilateral with sides each pair of opposite Regular Convex Irregular Concave sides parallel Rhombus: Parallelogram Rectangle: Parallelogram Square: Parallelogram with with equal sides with right angle equal sides and equal angles Key Points • A polygon with four sides is called a quadrilateral. • A quadrilateral with opposite pair of sides parallel • A Polygon in which all its interior angles are less than 1800 is called convex polygon. and diagonals bisecting each other is called parallelogram. • A parallelogram with equal sides is a rhombus. • A polygon with atleast one reflex interior angle is In rhombus, diagonals bisect each other at right angle. called a concave polygon. • A rhombus with each interior angle a right angle and diagonals of equal length is called a square. • A parallelogram with equal diagonals is called a rectangle. • A quadrilateral with exactly two pairs of equal con- secutive equal sides is called a kite. In a kite, diag- onals are perpendicular to one another. One of the diagonals bisect the other. • An equiangular and equilateral polygon is called a regular polygon. 18

3. Understanding Quadrilaterals Work Plan CONCEPT COVERAGE COVERAGE DETAILS PRACTICE SHEET Pre requisite knowledge: • Types of angle -acute, obtuse, straight, right, PS – 1 Angles Parallel lines Triangle reflex. and its properties • Parallel lines condition • Parallel lines and transversal and its properties • Angle sum property of a triangle • Exterior angle of a triangle Polygons • Definition of polygon PS – 2 • Types of polygon – convex and concave polygon. • Regular and irregular polygons • Angle sum property of polygon PS – 3 • Sum of all exterior angles of a triangle is 360 degrees Types of Quadrilaterals • Basic definition • Types of quadilaterals • Properties of angles of a quadrilateral PS – 4 • Properties of sides of quadrilaterals • Special types of parallelograms - Properties Worksheet for “Understanding Quadrilaterals” PS – 5 Evaluation with Self Check or ---- Self Evaluation Sheet Peer Check* 19

PRACTICE SHEET - 1 (PS-1) 1. A line has ______ end points. 2. An acute angle measures between _____ and ________. 3. Complementary of 700 is _____________. 4. If sum of two angles of a triangle are 600 are 900. Find the third angle. 5. Sum of all the angles of an obtuse angled triangle is ___________. 6. Find x and y. 7. Can a triangle be formed with sides 2cm, 3cm and 5 cm? 8. In a right angle triangle, the side opposite to right angle is called ___________. 9. The median is a line joining vertex of one side to ____________ of opposite side. 10. The sum of any two sides of a triangle is ______________ than the third side. PRACTICE SHEET - 2 (PS-2) 1. Identify the type of polygon. 20

PRACTICE SHEET - 3 (PS-3) 1. Find the value of x, y and z. 2. Find the value of x, y and z. 3. Find the value of x. 4. Find the value of x. 5. Find the value of x. 6. Find the value of x. 21

PRACTICE SHEET - 4 (PS-4) 1. A polygon with all interior angles less than 1800 is a ___________ polygon. 2. If the diagonals of a quadrilateral bisect each other then it is a __________. 3. A rhombus has all its ___________ equal. 4. The adjacent angles of rectangle are _________________. 5. A parallelogram with adjacent sides equal and unequal diagonals is ________. 6. The angles of a quadrilateral are in the ratio 0f 1:2:3:4. Find the smallest angle. 7. In a parallelogram if the measure of one angle is 600. Find the measure of other three angles. 8. If adjacent angles of parallelogram are in the ratio of 2:3, find the angles. PRACTICE SHEET - 5 (PS-5) I. Choose the correct option. 1. Which of these is a polygon? (A) (B) (C) (D)All of these 2. A line segment joining the opposite vertices of a polygon is called its ______. (A) side (B)edge (C)diagonal (D) Both (A) and (B) 3. Name the polygon with 8 sides. (A) Hexagon (B)Octagon (C) Decagon (D) Heptagon 4. A polygon with 5 sides has all its diagonals inside itself. What type of a polygon is it? (A) Convex polygon (B)Concave polygon (C) Regular polygon (D) Irregular polygon 5. Identify the characteristic of a regular polygon. (A) It is equiangular (B) It is equilateral (C) Both (A) and (B) (D) Neither (A) nor (B) 6. Find the measure of the angle marked ‘x’ in the given figure. (A) 50o (B) 130o (C) 70o (D) 60o 7. The quadrilateral with equal opposite sides, each of its angles measuring 90o and diagonals bisecting each other is a __________. (A) parallelogram (B) rhombus (C) kite (D) rectangle 8. The quadrilateral whose diagonals bisect each other perpendicularly is a ________. (A) square (B) rectangle (C) parallelogram (D) Trapezium 9. The quadrilateral with equal diagonals is a _______________. (A) rhombus (B) rectangle (C) parallelogram (D) All of these 10. What additional property must a parallelogram satisfy so that it becomes a rectangle? (A) Its diagonals are equal in length. (B) Each of its angles measure 90ᵒ. (C) Its diagonals bisect each other. (D) All of these II. Short Answer Questions. 11. Find the lengths of the diagonals in the given figure. 22

PRACTICE SHEET - 5 (PS-5) 12. Write the properties of a parallelogram. 13. In the given parallelogram, find the measures of the unknown angles, mentioning the properties used. III. Long Answer Questions. 14. Using relevant properties, find the remaining angles in the given parallelogram. 15. O is the midpoint of the hypotenuse of the right angled triangle ABC. Show that O is equidistant from its vertices, A, B and C. 23

SELF-EVALUATION SHEET Marks: 15 Time: 30 Mins 1. Adjacent sides of a rectangle are in the ratio 5:12, If the perimeter of the rectangle is 34 cm, find its length of its sides. (1 Mark) 6. ABCD is a parallelogram. Find x. (2 Marks) 2. The opposite angles of a parallelogram are (4x+5) and (6x-3). Find all the angles of the parallelogram. (1 Mark) 3. In parallelogram HOPE bisectors of angle H and 7. A diagonal and a side of a rhombus are equal. angle O meet each other at A, find the measure of angle HAE.  (1 Mark) Find the angles of rhombus. (3 Marks) 4. Find the number of sides of a regular polygon whose each exterior angle measures 600. (2 Marks) 8. Find the length of one of the diagonals of a rectangle whose sides are 10 cm and 24 cm. (3 Marks) 5. Two sticks each of length 5 cm are placed such that they bisect each other. What shape is formed by joining their end points? (2 Marks) 24

4. Practical Geometry Learning Outcomes At the end of this chapter, you will be able to: • Construct a quadrilateral when three sides and • Construct a quadrilateral when the lengths of four two included angles are given. sides and a diagonal are given. • Construct quadrilaterals of special cases. • Construct a quadrilateral when two diagonals and • Construct a quadrilateral when two adjacent three sides are given. sides and three angles are known. Concept Map Key Points • Five measurements can determine a quadrilateral uniquely. • A quadrilateral can be constructed uniquely if the lengths of its four sides and a diagonal are given. • A quadrilateral can be constructed uniquely if its two diagonals and three sides are known. • A quadrilateral can be constructed uniquely if its two adjacent sides and three angles are known. • A quadrilateral can be constructed uniquely if its three sides and two included angles are given. • A square can be constructed only with one side length given. • A rhombus can be constructed when length of two diagonals are given. 25

4. Practical Geometry Work Plan CONCEPT COVERAGE COVERAGE DETAILS PRACTICE SHEET Construction of quadrilaterals • Construction of a quadrilateral when the PS – 1 lengths of four sides and a diagonal are given Construction of quadrilaterals • Construction of a quadrilateral when two PS – 2 diagonals and three sides are given Construction of quadrilaterals • Construction of a quadrilateral when two PS – 3 adjacent sides and three angles are known Construction of quadrilaterals • Construction of a quadrilateral when three PS – 4 sides and two included angles are given • Special cases Worksheet for “Practical Geometry” PS – 5 Evaluation with self- check or Peer Self-evaluation Sheet check* 26

PRACTICE SHEET - 1 (PS-1) 1. Construct quadrilateral PQRS with PQ = 5.5 cm , QR= 6.5 cm, RS = 5 cm, SP = 7 cm and PR = 8 cm. 2. Construct quadrilateral ABCD with AB= 4.5 cm, BC= 5 cm, CD= 6 cm, DA= 5.5 cm and BD= 7.5 cm. 3. Construct a parallelogram ABCD with BC = 6 cm, CD = 4.5 cm and DB = 7.5 cm. 4. Construct rhombus PQRS with PQ = 5.5 cm and QS = 7 cm. PRACTICE SHEET - 2 (PS-2) 1. Construct quadrilateral PQRS with PQ = 5 cm, QR = 4 cm, PR = 5.5 cm, SP = 3.5 cm and SQ = 5 cm. 2. Construct quadrilateral ABCD with BC = 8.5 cm, CD = 6 cm, DA = 7 cm, BD = 11 cm and AC = 7 cm. 3. Construct the rhombus PQRS with PR = 6.6 cm and SQ = 7 cm. PRACTICE SHEET - 3 (PS-3) 1. Construct quadrilateral MORE with MO = 7cm, RO = 5.5 cm ∠M = 70°, ∠O = 110° and ∠R = 90°. 2. Construct a quadrilateral JUST where JU = 3.5 cm, US = 6.5 cm, ∠J = 75°, ∠U = 105° and ∠S = 60°. 3. Construct parallelogram MUST with MU = 6 cm, US = 7 cm and ∠S = 80°. PRACTICE SHEET - 4 (PS-4) 1. Construct a quadrilateral ABCD, where AB = 5 cm, BC = 6 cm, CD = 7.5 cm and ∠B = 100° and ∠C = 85°. 2. Draw a square of side 4 cm. 3. Construct a rhombus PQRS with PR = 5 cm and QS = 4 cm. [3 marks] 27

PRACTICE SHEET - 5 (PS-5) I. Short Answer Questions. 1. The rough diagram of construction of a quadrilateral is given. Write the condition that can be used to construct it. 2. Write the condition that can be applied when a quadrilateral is constructed, given its three sides and two diagonals. 3. What are the special quadrilaterals that can be drawn without knowing 5 measurements? Give the measurements needed to construct them. 4. List the different conditions that help us to construct a unique quadrilateral. II. Long Answer Questions. 5.Given PQ = 5 cm, QR = 4 cm, PS = 6.5 cm, ‘P 70q and ‘Q 115q , construct the quadrilateral PQRS explaining the steps of construction. 6. Given AB = 5.5 cm, BC = 4.5 cm, ‘A 85q , ‘B 75q and ‘C 110q , construct the quadrilateral ABCD explaining the steps of construction. 7. Construct a square of side 5 cm. Write the construction steps. 8. Construct a rectangle of length 7 cm and width 4.5 cm. Write the construction steps. 28

SELF-EVALUATION SHEET Marks: 15 Time: 30 Mins 1. During the construction of a quadrilateral for 5. Draw a square of side 5 cm. (3 Marks) which 2 sides and 3 angles are known, how is the 4th point plotted? (1 Mark) 2. A minimum of how many triangles are required to construct a triangle by putting together triangles. (1 Mark) 6. Construct a rhombus PQRS with PR = 6cm and QS = 5 cm. (3 Marks) 3. How many quadrilaterals can be constructed with the following data? Quadrilateral PQRS with PQ = 4.5 cm, ‘P 70q , ‘Q 100q , ‘R 80q and ‘S 80q . (2 Marks) 7. Construct a quadrilateral PQRS where PQ = 3 cm, QR = 5 cm, RS = 4 cm, PS = 4.5 cm and PR = 6 cm. (3 Marks) 4. Given length of two sides of a quadrilateral, what kind of quadrilateral can be constructed and how? (2 Marks) 29

5. Data Handling Learning Outcomes At the end of this chapter, you will be able to: • Understanding and analyzing the graph. • Group the data using tally marks, group the data in • Represent the data in the form of pie chart. • Convert the pie chart to find the data. the form of grouped frequency distribution table. • Represent the data graphically using either bar graph or histogram. Concept Map Key Points Team Number of People Pune 7 • What is Data? Mumbai 5 A systematic record of facts or different values of Kolkata 3 a quantity is called data. Delhi 2 Data mostly available to us in an unorganized Hyderabad 2 form is called raw data. Bangalore 1 Arranging data in an order to study their salient features is called presentation of data. The number of people is called the frequency. Frequency Distribution Table • Frequency gives the number of times that a Data is given to us in unorganized form. We organize them to make it easy to read. Let’s particular entry occurs. understand it with an example 20 people were Table that shows the frequency of different asked for their Favourite IPL team, the answer is values in the given data is called a frequency Pune, Mumbai, Mumbai, Kolkata, Delhi, Kolkata, distribution table. Pune, Mumbai, Hyderabad, Bangalore, Mumbai, • Bar Graph Pune, Delhi, Mumbai, Pune, Kolkata, Pune, Pune, A bar graph is a pictorial representation of data Hyderabad, Pune. in which rectangular bars of uniform width are It will be difficult to read this data, so we will drawn with equal spacing between them on one organize this data into table format. axis, usually the x axis. The value of the variable is shown on the other axis that is the y axis. We can represent frequency distribution table on bar graph also. 30

5. Data Handling • Grouped frequency distribution the class interval. Also, there is no gap between Sometime data is very huge and it is not easy to the bars as there is no gap between the class create frequency distribution table. Also there will intervals. be lot of categories so difficult to distinguish. • Circle Graph or Pie-chart let’s understand this with an example. A circle graph shows the relationship between a A class of 50 students was given Physics test of whole and its part. The whole circle is divided into maximum marks 60. Here is the test score of the sectors. The size of each sector is proportional to students 20, 21, 22,22, 23, 25, 26, 27, 27, 26, 27, 26, the activity or information it represents. 29, 26, 27, 25, 25, 30, 51, 55, 46, 47, 48, 41, 42, 31 , 34, 35, 35, 36, 36, 37, 37, 35, 37, 39, 39, 37, 36, 35, Chance or Probability 36, 36, 37, 38, 38, 39, 39, 43, 44, 44. • Random Experiment Class Marks Frequency A random experiment is one whose outcome 20-25 5 cannot be predicted exactly in advance. 25-30 12 Example Throwing a dice, Tossing the coin 30-35 3 • Equally Likely outcome 35-40 20 Outcomes of an experiment are equally likely if each has the same chance of occurring. 40-45 5 Example 45-50 3 In tossing the coin, both head and tail can come 50-55 2 equally likely If we draw the frequency distribution based on In throwing the dice, all the number 1, 2, 3, 4, 5, 6 individual marks, it will difficult to understand can come equally likely the data, so for convenience we can group the • Event marks in equal interval and draw the frequency One or more outcomes of an experiment make an distribution like below. event. The above table is called grouped frequency Example distribution. Getting a tail in tossing a coin is an event 20-25, 25-30 are called the class interval. Getting a number 1 or getting number 2 in a throw In 20-25 class interval, 20 is called lower class of dice are also event limit and 25 is called the upper class limit. Getting an odd number in a throw of dice is also The common observation like 20, 30, etc. belongs an event. The event will contain 1,3,5 as outcome to the higher class interval. So 25 will belong to 25-30. • Probability Probability is calculated as • Important Definition from above learning A table that shows the frequency of groups of Probability�o� f an event = Number�o� f outcomes�tha� t make�a� n event values in the given data is called a groPurpoebdability�o� f Total�numbe� r of �outcome� s of �th� e experimen frequency distribution table. Number�o� f outcomes�tha� t make�a� n event an�event = Total�numbe� r of �outcome� s of �th� e experiment The groupings used to group the values in given This is applicable when the all outcomes are data are called classes or class-intervals. The number of values that each class contains is equally likely. called the class size or class width. The lower value in a class is called the lower class limit. The higher value in a class is called the upper class limit. The common observation will belong to the higher class. • Histogram Grouped data can be presented using histogram. Histogram is a type of bar diagram, where the class intervals are shown on the horizontal axis and the heights of the bars show the frequency of 31

5. Data Handling Work Plan CONCEPT COVERAGE COVERAGE DETAILS PRACTICE SHEETS PS – 1 Date-grouping of data • Ungrouped frequency distribution • Grouped frequency distribution PS – 1 Graphical representation • Histogram PS – 2 • Reading and analyzing histogram PS – 3 PS – 4 Graphical representation • Pie chart Self-evaluation • Analyzing pie chart Probability • Probability Worksheet for “Data Handling” Evaluation with self-check or Peer check* 32

PRACTICE SHEET - 1 (PS-1) 1. The marks obtained by 35 students (out of 100) in a class is given below. Using tally marks make a frequency distribution table to represent the following data: 25, 14, 90,25,4,68, 74,89,42,35, 38,12,7,19,50, 74,58,69,25,35,15, 16,79,92,94,23,72, 36,38, 19,78, 80,65,45, 28 2. The number of absentees in class VIII was recorded in a particular week. Represent this data on the bar graph. Days Mon. Tues. Wed. Thurs. Fri. Sat. Number of 130 120 135 130 150 80 Absentees (a) On which day the maximum and minimum students were absent? (b) How many students were absent on Wednesday and Tuesday? (c) On which days the same number of students was absent? 3. The following data represents the sale of refrigerator sets in a showroom in first 6 months of the year. Months Jan Feb March April May June No. of 20 25 15 40 35 30 Refrigerators Sold Draw the bar graph for the data given and find out the months in which the sale was minimum and maximum. 4. Understand the following graph and answer the following: (i) Which year has the highest and lowest population? (ii) What is the difference between the population in year 2009 and 2005 33

PRACTICE SHEET - 1 (PS-1) 5. Answer the following questions based on the graph given: (i) In which subject was the marks obtained maximum? (ii) What is the difference between the marks obtained in highest and lowest marks obtained? (iii) What is the mean marks obtained by the student? 34

PRACTICE SHEET - 2 (PS-2) 1. In a zoological park there are 1000 creatures as per the following table given below: Beast Other land Birds Water Reptiles animal animals 225 animals 50 150 400 175 Represent the above data by a pie chart. 2. The following table gives the number of different fruits kept in a hamper. Type of Mangoes Apples Oranges Coconuts Pome- fruit 26 30 21 granates Number 56 Represent the above data by a pie chart. 3. The following table shows the percentage of buyers of four different brands of bathing soaps. Brand ABCD Percentage of buyers 20% 40% 25% 15% Represent the above data by a pie chart. 4. Read the pie chart and answer the following questions. The following pie chart represents the monthly expenditure of a man, who earns Rs 36000 per month, (i) How much money does he save in a month? (ii) Find the amount spent by him on food. (iii) Find the amount spend by him on education for three months. . 35

PRACTICE SHEET - 2 (PS-2) 5. Pie charts below show the types of food consumed by people in China, India and across the world when 10000 people were surveyed. Based on the pie charts answer the following. Meat, Fish and Eggs (i) How many people and which country consume maximum amount of meat, fish and eggs? (ii) How many people across the world consume nuts and seeds? (iii) How many people in China consume meat, fish and eggs? (iv) How many people in India consume processed food? (v) What is the difference in number of people consuming vegetables and fruits in India and China PRACTICE SHEET - 3 (PS-3) 1. When a dice is thrown, list the outcomes of an event getting (i) A number less than 4 (ii) A number greater than 3 (iii) A non prime number (iv) Multiple of 3 2. Cards numbered 1 to 10 are placed in random order. Find the probability of getting (i) An odd number (ii) an even number (iii) multiple of 2 (iv) even number less than 5 3. A bag contains 5 red balls, 4 blue balls and 6 black balls. Find the probability of getting a red ball, a black ball. 36